Mathematics Question and Solution
Calculating x, the radius of the big quarter circle.
a = ½(90)
a = 45°
a is half angle DBE.
b = ½(180-45)
b = 67.5°
b is angle BDF.
c = (x+1) units.
c is AB.
d = (x-1) units.
Therefore, x is;
tan67.5 = (x+1)/(x-1)
x+1 = (tan67.5)x-tan67.5
1+tan67.5 = (tan67.5)x-x
((tan67.5)-1)x = 1+tan67.5
x = (1+tan67.5)/((tan67.5)-1)
x = (1+√(2)) units.
x = 2.41421356237 units.
Again, x is the radius of the big quarter circle.
